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Консультация № 197689
04.02.2020, 22:43
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
На рисунке 14, в изображён прямой параллелепипед ABCDA1B1C1D1, объем которого равен 80см3. Площадь квадрата АВСD равна 16см2. Вычислите длину диагонали большей боковой грани призмы ABDA1B1D1.
На рисунке 14, в изображён прямой параллелепипед ABCDA1B1C1D1, объем которого равен 80см3. Площадь квадрата АВСD равна 16см2. Вычислите длину диагонали большей боковой грани призмы ABDA1B1D1.
Обсуждение
05.02.2020, 15:35
общий
Адресаты:
Для начала ответьте на два простых вопроса:
1) Если площадь основания равна 16, а объём - 80, то чему равна высота?
2) Если площадь квадрата равна 16, то чему равна его сторона?
1) Если площадь основания равна 16, а объём - 80, то чему равна высота?
2) Если площадь квадрата равна 16, то чему равна его сторона?
09.02.2020, 18:51
общий
это ответ
Здравствуйте, svrvsvrv!
Объём прямого параллелепипеда равен произведению площади основания на высоту. В данном случае объём равен 80 см3, а площадь основания - 16 см2, поэтому высота параллелепипеда (а также искомой призмы и всех её боковых граней) составит 80/16 = 5 см. Самой большой боковой гранью призмы является, очевидно, BDD1B1. Её высота нам уже известна (BB1 = DD1 = 5 см), а основанием является отрезок BD - диагональ квадрата ABCD с площадью 16 см2, поэтому AB = AD = 4 см, BD = 4[$8730$]2 см? и длина диагонали прямоугольника BDD1B1 составит
Объём прямого параллелепипеда равен произведению площади основания на высоту. В данном случае объём равен 80 см3, а площадь основания - 16 см2, поэтому высота параллелепипеда (а также искомой призмы и всех её боковых граней) составит 80/16 = 5 см. Самой большой боковой гранью призмы является, очевидно, BDD1B1. Её высота нам уже известна (BB1 = DD1 = 5 см), а основанием является отрезок BD - диагональ квадрата ABCD с площадью 16 см2, поэтому AB = AD = 4 см, BD = 4[$8730$]2 см? и длина диагонали прямоугольника BDD1B1 составит
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